Exercise 5.3.5

Avg difficulty 3.0

Suppose $V,W$ are subspaces of $\mathbb{R}^{n}$ . Let $V\cap W$ be the set of all vectors that are in both $V$ and $W$ . Show that $V\cap W$ is also a subspace.

Selinger, Matrix Theory and Linear Algebra, Spans, linear independence, and bases in Rn, Subspaces of R^n, Exercise 5.3.5

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Adapted from Matrix Theory and Linear Algebra © 2017–2026 Peter Selinger, Lyryx Learning, and Ken Kuttler. Licensed under CC BY 4.0. Source: Matrix Theory and Linear Algebra. Imported at revision d74bc3a.